Problem: Solve for $x$ and $y$ using elimination. ${4x-6y = -38}$ ${-3x+5y = 33}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${20x-30y = -190}$ $-18x+30y = 198$ Add the top and bottom equations together. $2x = 8$ $\dfrac{2x}{{2}} = \dfrac{8}{{2}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {4x-6y = -38}\thinspace$ to find $y$ ${4}{(4)}{ - 6y = -38}$ $16-6y = -38$ $16{-16} - 6y = -38{-16}$ $-6y = -54$ $\dfrac{-6y}{{-6}} = \dfrac{-54}{{-6}}$ ${y = 9}$ You can also plug ${x = 4}$ into $\thinspace {-3x+5y = 33}\thinspace$ and get the same answer for $y$ : ${-3}{(4)}{ + 5y = 33}$ ${y = 9}$